• bending-unbending transition
• interfaces
• nonlocality
• surfaces
• wettability
• wetting transitions

A long-standing problem of statistical mechanics, the 3D critical wetting with short-range forces has been solved recently by a new interfacial hamiltonian model - the Nonlocal Model. The NL Model was heuristically derived starting from a microscopic LGW-Hamiltonian through a careful coarse-grain procedure of tracing out the bulk degrees of freedom, based on a recepit proposed by Fisher-Jin in 1991. A new features presented with the NL Model are easily handable diagrammatic expansions for the observables.

The purpose of this thesis is to shed a new light on the theoretical foundations of the NL Model, for which a new rigorous variational derivation is given. In the new formalism is possible to work out exact considerations whose formal solution leads to new exact diagrammatic expansions.

Within this new framework, the analysis of geometrically patterned substrates with chemical heterogeneities is easily implementable. The planar substrate with two different chemical species periodically arranged in strips is numerically studied with the BEM. In our investigation no evidence of the the first-order bending transition was found to exist; nevertheless a continuous crossover between thin-thick films is observed for the first time. A discussion on forthcoming developments of this rapidly evolving research is given.